updated 12/11/2013 AT 12:00 PM ET
•originally published 12/11/2013 AT 2:00 PM ET
Kutcher Tweeted a pic that appears to be himself and his girlfriend kissing under what seems to be the neon sign outside the famed Sun Studios in Memphis. “Sunset #nofilter,” he wrote.
By all accounts, their romance is going strong. Kutcher accompanied Kunis to her brother’s wedding last weekend, and a source tells PEOPLE that now that his divorce from Demi Moore is final, Kutcher is ready to make Kunis his wife.
“Ashton and Mila have talked about getting engaged and married for quite a while,” said the source close to Kutcher. “He wants to get engaged during the holidays.”